SuNeRF-CME: Physics-Informed Neural Radiance Fields for Tomographic Reconstruction of Coronal Mass Ejections

Technical Summary: SuNeRF-CME

Problem Statement
Coronal Mass Ejections (CMEs) pose significant space weather risks, necessitating accurate 3D characterization of their plasma density, propagation direction, and velocity. While white-light coronagraphs provide direct monitoring of CMEs via Thomson-scattered light from free electrons, reconstructing the 3D plasma distribution from 2D imaging data is inherently challenging. The problem is ill-posed due to the optically thin nature of the plasma, the complex viewpoint dependence of Thomson scattering, and the scarcity of simultaneous viewpoints (often limited to two or three). Traditional methods, such as the Graduated Cylindrical Shell (GCS) model or stereoscopic triangulation, often rely on geometric approximations or static assumptions that fail to capture complex deformations, internal structures, or time-dependent evolution, leading to systematic deviations and "ghost trajectories."

Methodology
The authors introduce SuNeRF-CME (Sun Neural Radiance Fields for CMEs), a framework that combines Neural Radiance Fields (NeRFs) with Physics-Informed Neural Networks (PINNs) to perform 3D tomographic reconstruction of the heliosphere.

• Neural Representation: Instead of using explicit grids, the 3D volume is represented by a neural network (specifically a SIREN architecture) that maps spatiotemporal coordinates $(x, y, z, t)$ to physical quantities: logarithmic electron density ($\ln \rho$) and velocity vectors ($\vec{v}$). This provides a memory-efficient, continuous implicit parameterization of the 4D volume.
• Forward Model: The method employs a physically consistent forward model based on Billings (1966) to simulate Thomson scattering. It calculates total brightness ($tB$) and polarized brightness ($pB$) by integrating the modeled electron density along lines of sight, accounting for the scattering angle, solar limb darkening, and the finite angular extent of the solar disk.
• Physics-Informed Constraints: To mitigate the ill-posed nature of the inversion caused by sparse viewpoints, the framework incorporates physical constraints via a PINN approach. The loss function includes:
  • Continuity Equation: Enforcing mass conservation ($\partial_t \rho + \nabla \cdot (\rho \vec{v}) = 0$) to couple density dynamics with velocity.
  • Radial Regularization: Constraining the background solar wind to be approximately radial.
  • Velocity Bounds: Enforcing solar wind speeds within a realistic range (200–800 km s$^{-1}$) to suppress unphysical static clouds or ghost trajectories.
• Optimization: The network is trained from scratch for each specific CME event by minimizing a combined loss function comprising image-based errors (logarithmic $L_2$ norm of $tB$, $pB$, and their ratio) and physics-based residuals.

Key Contributions

1. First Physics-Informed NeRF for CMEs: This work presents the first implementation of a Physics-Informed Neural Radiance Field specifically for CME tomography, adapting NeRFs from the EUV domain to white-light coronagraphic data.
2. Sparse Viewpoint Reconstruction: The method demonstrates the ability to reliably reconstruct 3D CME structures from as few as two viewpoints, a scenario where classical tomography often fails.
3. Integration of Dynamics: Unlike static reconstruction methods, SuNeRF-CME explicitly models the time-dependent evolution of the plasma, capturing deformations and propagation dynamics without relying on solar rotation for additional constraints.
4. Validation Framework: The study utilizes the "CME Challenge" dataset (synthetic observations from the GAMERA-Helio model) to rigorously quantify performance against ground-truth electron density distributions across various observer configurations.

Results
Using synthetic observations, the authors evaluated the method's performance across different viewpoint configurations:

• Parameter Estimation: From two viewpoints separated by 60°, the method achieved mean errors of 3.39 ± 1.94° in latitude, 1.76 ± 0.79° in longitude, and 3.01 ± 1.94% in shock-front velocity. These results represent an improvement of roughly a factor of two to four over traditional GCS fitting results reported in previous literature.
• 3D Structure Recovery: The model successfully reconstructed the "three-part structure" (bright core, dark cavity, bright front) and internal plasma variations of simulated CMEs from two viewpoints. It captured deformed CME fronts and shock front localization, though background solar wind structures remained more challenging to resolve with sparse data.
• Viewpoint Dependence: Performance improved with the number of viewpoints (correlation coefficient increasing from 0.92 for three viewpoints to 0.99 for all available viewpoints). Reconstructions were found to be less reliable within the observer plane (ecliptic) compared to out-of-plane views.
• Role of Polarization: The inclusion of polarized brightness ($pB$) significantly improved reconstruction quality. A single $pB$ observation combined with total brightness ($tB$) from other viewpoints could effectively substitute for an additional $tB$-only viewpoint, reducing line-of-sight ambiguities.
• Physics Constraints: Ablation studies confirmed that physics-informed losses are critical; removing them led to unphysical drifts in propagation direction and mass, while moderate weighting (10$^{-2}$–10$^{-1}$) yielded optimal stability.
• Noise Robustness: The method remained stable up to noise levels of 5% of the mean brightness (SNR = 20), though performance degraded in faint outer regions where signal-to-noise ratios drop.

Significance and Claims
The paper claims that SuNeRF-CME demonstrates the potential of physics-informed radiance-field methods for CME tomography. By treating the neural network as a continuous function representation rather than a generative model trained on a population, the method directly reconstructs specific scenes from available multi-vantage data. The authors emphasize that this approach provides a data-driven, event-specific solution that overcomes the limitations of geometric approximations and static assumptions.

The study concludes that while current results are limited to synthetic data, the framework paves the way for future extensions to real observational data and space weather applications. The authors note that the method's ability to integrate physical constraints directly into the optimization process allows it to handle sparse data and noisy inputs more robustly than classical inversion techniques, offering a promising path toward real-time 3D monitoring of heliospheric plasma dynamics.